Well…not really zero words…closer to 100,000, in fact. But the main point of Dana Mackenzie’s beautiful book about beautiful mathematics is his combination of illustrations, numbers, and the equations relating those numbers to each other. Essentially, The Universe in Zero Words is a history of math — but it’s history with a twist. Mackenzie explicates 24 important episodes, each containing an important equation that helped to explain the universe in some way. Usually we’re talking about mathematical theory, not directly about applications. Nevertheless, the “unreasonable effectiveness of mathematics” almost guarantees that the theory will end up being applied in practical uses.
Before going into any detail about the specific equations, I have to say something about the gorgeous illustrations. It’s rare to see such a well-produced collection of art, photographs, and drawings, mostly in full color, as illustrations in a math book. It would be worth reading the book for the pictures alone. Here are a couple of examples: a picture of Turkish tiles illustrating group theory, followed by a 16th-Century etching called “Allegory of Geometry”:
The second of these illustrations accompanies a fascinating chapter called “The Geometry of Whales and Ants.” As you probably can’t tell from the title, the topic of the chapter is the development of non-Euclidean geometries, including hyperbolic (the geometry of whales) and elliptic (the geometry of ants). While it’s easy to see why ants would favor elliptic geometry, it was a complete mystery to me why whales would favor elliptic. But then I read the chapter, and now I am enlightened. Read the book, and you’ll be enlightened too.